Possible press release about voting paper by Warren D. Smith... ============================================================= With the battle between presidential candidates A.Gore and G.W.Bush over tiny vote margins in Florida growing ever more tiresome, the weary public must be asking themselves: "Isn't there a better way to run an election?" The problem is not just the tactics of Bush, Gore, and their lawyers. An earlier problem had been the entry into the race of third party candidate Ralph Nader. Although only about 2-3% of voters nationwide voted for Nader, this percentage far exceeds the difference between the numbers of Bush and Gore votes - especially in the critical state of Florida. Polls indicate that 40% of Nader voters would have voted Gore, 20% would have voted Bush, and the remaining 40% other (or no vote) - enough that Gore clearly would have won - had Nader not been in the race. However, at present it appears that Bush has won. If so, that means that the USA was deprived of the candidate more Americans wanted than the winner, by the very voting system itself. This suggests that the voting method used in the USA has somehow been mathematically ineffective and unfair to Gore. Looking more deeply, it has also been unfair to Nader and/or other 3rd party candidates, since millions of would-be Nader voters felt "tactically forced" to betray their favorite and to "dishonestly" vote for their nonfavorite: Gore or Bush. Looking still more deeply, the candidate Bush had defeated in the earlier Republican "primary" election, John McCain, enjoyed (polls indicated) more combined voter support than either Bush or Gore. If so, the voting system has acted to deprive Americans of a choice they wanted more than the winner, not once, but twice, in the same election. So voting systems can and do pick the apparently "wrong" winner. Does this invalidate the whole idea of democracy? How flawed must voting systems be? What can mathematics tell us about this? Recent work by mathematician Warren D. Smith of NEC Research Institute indicates that the voting systems used by all democracies are considerably more flawed than they need be. Smith claims that the "cumulative historical damage caused by the use of mathematically non-optimal voting systems, has been tremendous." Smith advocates a system he calls "range voting." In this system, you provide a k-tuple of real numbers, each in some fixed range (Smith uses -1 to 1, but 0-1 and 0-10 are other popular choices; all are equivalent) as your "vote" in a k-candidate election. For simplicity, let us, like Olympic figure skating judges, use the range 0-10. Consider a 4-way election with candidates (Buchanan, Bush, Gore, Nader). You could provide, as your vote, the 4-tuple (0, 2, 9, 10). All the vote-tuples are then added up, and the winner is the candidate with the largest total. For example, if this vote and also somebody else's vote (6, 10, 0, 8) were added, we would get (6, 12, 9, 18). The largest total would be 18 so (if these were the only two voters), Nader would be the winner. Notice that, in range voting, a Nader voter COULD indicate his preference for Gore over Bush (or vice versa) whereas, in the usual "plurality" system used in the election, it was impossible for a Nader voter to indicate that preference in any way. Nor need a vote for Nader be "wasted" in range voting. Thus, range voting's net effect is to give the voter more ability to express more of his feelings more honestly, without being "tactically misguided." With more voters expressing more feelings more honestly, hopefully the election results reflect what the voters want, more accurately, more often. Smith has proved theorems saying, roughly, that range voting is the best possible voting system within a wide class of possible voting systems which he calls "COAF systems." (COAF stands for "Compact set based One-vote Additive Fair"). By "best," Smith means that range voting, roughly, offers voters both the opportunity and the incentive to express the most possible information in their vote. But, the evidence for the superiority of Range Voting that Smith considers MOST convincing, is not a theorem, but rather a computer simulation of 31 kinds of voting systems in millions of artificial "elections," each with 2-5 contenders. The voting systems Smith tried (besides range voting) include: * plain plurality (the most traditional system), * "bullet" voting (which is like plurality, except instead of casting a vote FOR your favorite candidate, you cast one AGAINST the candidate you hate the most! The candidate hit by the fewest such "bullets" wins), * The "Borda count" system, invented by French scientist Jean-Charles de Borda in 1770, where you rank the candidates in order of preference as your vote (the rankings are added). For example, with N candidates, your first preference gets N-1 points, your second gets N-2, etc.; the candidate you dislike most gets 0. The highest point-getter is the winner. Borda's method was used in votes in the French Academy of Sciences for many years until Napoleon introduced a different method. * The Condorcet "least reversal" system advocated by Borda's rival the Marquis de Condorcet, in 1785, but unfortunately largely abandoned. In this system, the winner is the one who would require the fewest reversals of voter pairwise preferences in order to win every pairwise (2 candidate) election. (Voters give a list of of all the candidates ordered by preference, as their vote.) * Two variants of the "single transferable vote" (STV) system. In this system, the candidate with the fewest votes loses, and then all votes for losing candidates are "transferred" to the next candidate on a ordered list supplied by each voter. Such elimination-rounds continue until only one non-losing candidate remains. This system was invented by British politician Thomas Hare in about 1850 and praised in the writing of John Stuart Mill, who called Hare "a man of great capacity, fitted alike for large general views and for the contrivance of practical details" and said the "transcendant advantages" of Hare's plan were "so numerous... that, in my conviction, they place Mr. Hare's plan among the very greatest improvements yet made in the theory and practice of government." Hare's method is presently used to elect some Australian representatives and is used in national elections in Ireland, where it is specified in the (1937) constitution. In two nationwide referendums (in 1959 and 1968) the Irish were offered the option of abandoning the STV system, and both times chose to keep it. * "Approval voting" where you "approve" or "disapprove" of each candidate, and the most-approved candidate wins. (This method was invented independently by several theorists in the 1970s, including S.J.Brams, a political science professor at NYU. It is used in the internal elections of a number of professional societies, including the International society of Electrical & Electronics Engineers.) and various others. Using each voting system, Smith's computer-generated "voters" voted for computer generated "candidates." Each voter had a "utility" number for each candidate saying how much that candidate's election would benefit him. All these numbers, too, were artificially computer generated, by a choice of several different randomized methods. "This is largest-ever simulation trying many different voting systems on the same elections, and the only one which involved range voting as a participating system," said Smith. "Unlike in real elections involving humans," Smith explains, "in my computer generated elections we actually KNOW the true, private, `Bayesian Utility values' of every candidate inside every voter's mind. So we can, after the election is over, accurately assess the damage - the exact amount, measured as a summed utility, by which the whole of society will suffer because of occasional election of a less-than-best candidate." (Statisticians call this "damage" the "Bayesian regret.") Smith's voters could employ a number of "strategies" when choosing their vote. For example, they could be "honest." Or, they could be "rational" and seek to maximize the positive impact of their vote - which might (like the decision to "betray Nader" made by millions of Americans) involve casting a "dishonest" vote not accurately reflecting that voter's preferences. After about a day of number crunching, the computer reported the results, which favored Range Voting over all the other systems tried, both for honest voters, and for strategic voters. "The computer simulations tell us that, by adopting plurality voting, the USA and other democracies are `suffering' from non-optimal election results more than they would have suffered with range voting," said Smith. How much more? "On average, by a factor of 3-10 more assuming honest voters (depending on the number of candidates in the election and other variables), and by a factor between 2.1 and 2.9 for strategic voters." What about the Australian/Irish system and the "Borda count"? Smith: "These are about 2 times worse than range voting, for strategic voters, and about 2-7 times worse, for honest voters. I was quite surprised at the resounding superiority of range voting over all the other methods. Because of my theorems, I expected range voting to be the best voting system, or to at least to be comparatively good, in a good fraction of my computer generated elections. But in fact, it was THE best system in 144 different kinds of elections - that is, EVERY kind I tried." 144 different kinds of elections? "The different kinds arise from choosing different numbers of voters, different numbers of candidates, or different ways of generating the utility numbers in each voter's head. I tried 144 different combinations of these factors, doing 144 different runs of the computer program," Smith explained. But perhaps the fact that range voting is 2-10 times better than plurality voting does not really matter because plurality voting hardly ever gets it wrong anyway? Does this matter in the real world? How much damage is really caused by poor voting systems? "You can get an idea of the scale of the damage by considering the Bayesian regret of the WORST possible election system - namely - the candidate who is the worst for society is automatically elected by my computer. The table shows that plurality voting causes 30% of that amount of damage if the voters act strategically. This is 60% of the damage caused by choosing a random candidate. I think that amount of damage is pretty significant." --------------TABLE-------------------------------------------- Average damage (Bayesian regret) caused by various voting systems in 200-voter, random utility elections with 5 candidates. (Scaled to make the damage caused by WORST candidate's election be 100.) --------------------------------------------------------------- Elect Worst candidate 100 Elect random candidate 50 Range voting ("honest" voters) 1.7 Range voting ("strategic" voters) 10 Plurality voting (honest) 17 Plurality voting (strategic) 30 STV (Australian/Irish system; honest) 10 STV (Australian/Irish system; strategic) 30 Bullet voting (honest voters) 18 Bullet voting (strategic voters) 49.9 --------------------------------------------------------------- In what ways would the political scene change if Range Voting were adopted? First, most analysts suspect that the grip of the "two party system" would weaken and third parties would gradually become relatively more powerful. Second, it is suspected that voter turnout (which in the last two presidential election years has been about 49 and 51% in the USA - and only about 36% in nonpresidential election years) would increase under range voting because more voters would feel less impotent, less forced to dishonestly support candidates they dislike, and more able to express their feelings in their vote. For example, turnouts in Irish elections, run under the more-expressive STV system, are usually about 80%, far higher than in USA elections and also higher than the turnouts in most other European countries, which are usually about 70%. ===end of press release.=================================================